Tính hợp lí :
A, 12x65 - 15x3 + 15 x 38
B, 24x13,5+24x0,42-24x3,92
C, 42x14+84x32-42x28
D, 45x16 - 90 + 45x76
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Vì x=14 nên x+1=15
Thay 15=x+1 vào A(x) Ta có:
A(x)= x^15-(x+1)x^14+(x+1)x^13-(x+1)x^12+...+(x+1)x^3-(X+1)^2+(x+1)x-15
=x^15-x^15-x^14+x^14+x^13-x^13-...+X^4+x^3-X^3-x^2+x^2-x-15
=x-15
=> A(14)=14-15=-1
Vậy A(14)=-1
k mình nha
\(A=\frac{9}{15.18}+\frac{9}{18.21}+.....+\frac{9}{89.92}\)
\(A=3.\left(\frac{3}{15.18}+\frac{3}{18.21}+....+\frac{3}{89.92}\right)\)
\(A=3.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+......+\frac{1}{89}-\frac{1}{92}\right)\)
\(A=3.\left(\frac{1}{15}-\frac{1}{92}\right)\)
\(A=3.\frac{77}{1380}=\frac{77}{460}\)
Đặt \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(\Leftrightarrow\)\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(\Leftrightarrow\)\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(\Leftrightarrow\)\(2A=1-\frac{1}{3^8}\)
\(\Leftrightarrow\)\(2A=\frac{3^8-1}{3^8}\)
\(\Leftrightarrow\)\(A=\frac{3^8-1}{3^8}:2\)
\(\Leftrightarrow\)\(A=\frac{3^8-1}{3^8}.\frac{1}{2}\)
\(\Leftrightarrow\)\(A=\frac{3^8-1}{2.3^8}\)
b) Đặt \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^8}\)
\(\Rightarrow\)\(3A=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^7}\)
\(\Rightarrow\)\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^8}\right)\)
\(\Rightarrow\)\(2A=1-\frac{1}{3^8}\)
\(\Rightarrow\)\(A=\frac{1-\frac{1}{3^8}}{2}\)
f(1) = 4.14 - 31.13 + 4.12 + 15 = 4 - 31 + 4 + 15 = -8
f(-1) = 4.(-1)4 - 31.(-1)3 + 4.(-1)2 + 15 = 4 + 31 + 4 + 15 = 54